selective-0.7: Selective applicative functors

Copyright | (c) Andrey Mokhov 2018-2023
License | MIT (see the file LICENSE)
Maintainer | andrey.mokhov@gmail.com
Stability | experimental
Safe Haskell | Safe-Inferred
Language | Haskell2010

Control.Selective.Rigid.Freer

Contents

- Free rigid selective functors
- Static analysis

Description

This is a library for selective applicative functors, or just selective functors for short, an abstraction between applicative functors and monads, introduced in this paper: https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors.pdf.

This module defines freer rigid selective functors. Rigid selective functors are those that satisfy the property `<*> = apS`. Compared to the "free" construction from Control.Selective.Rigid.Free, this "freer" construction does not require the underlying base data type to be a functor.

Synopsis

- data Select f a where
  - Pure :: a -> Select f a
  - Select :: Select f (Either (x -> a) a) -> f x -> Select f a
- liftSelect :: f a -> Select f a
- getPure :: Select f a -> Maybe a
- getEffects :: Functor f => Select f a -> [f ()]
- getNecessaryEffect :: Functor f => Select f a -> Maybe (f ())
- runSelect :: Selective g => (forall x. f x -> g x) -> Select f a -> g a
- foldSelect :: Monoid m => (forall x. f x -> m) -> Select f a -> m

# Free rigid selective functors

data Select f a where Source #

Free rigid selective functors.

Constructors

Pure :: a -> Select f a |
Select :: Select f (Either (x -> a) a) -> f x -> Select f a |

#### Instances

Instances details

Applicative (Select f) Source # |
Instance details Defined in Control.Selective.Rigid.Freer Methods pure :: a -> Select f a Source # (<*>) :: Select f (a -> b) -> Select f a -> Select f b Source # liftA2 :: (a -> b -> c) -> Select f a -> Select f b -> Select f c Source # (*>) :: Select f a -> Select f b -> Select f b Source # (<*) :: Select f a -> Select f b -> Select f a Source #
Functor (Select f) Source # |
Instance details Defined in Control.Selective.Rigid.Freer Methods fmap :: (a -> b) -> Select f a -> Select f b Source # (<$) :: a -> Select f b -> Select f a Source #
Selective (Select f) Source # |
Instance details Defined in Control.Selective.Rigid.Freer Methods select :: Select f (Either a b) -> Select f (a -> b) -> Select f b Source #

liftSelect :: f a -> Select f a Source #

Lift a functor into a free selective computation.

# Static analysis

getPure :: Select f a -> Maybe a Source #

Extract the resulting value if there are no necessary effects.

getEffects :: Functor f => Select f a -> [f ()] Source #

Collect all possible effects in the order they appear in a free selective computation.

getNecessaryEffect :: Functor f => Select f a -> Maybe (f ()) Source #

Extract the necessary effect from a free selective computation. Note: there can be at most one effect that is statically guaranteed to be necessary.

runSelect :: Selective g => (forall x. f x -> g x) -> Select f a -> g a Source #

Given a natural transformation from `f` to `g`, this gives a canonical natural transformation from `Select f` to `g`.

foldSelect :: Monoid m => (forall x. f x -> m) -> Select f a -> m Source #

Concatenate all effects of a free selective computation.